US9123156B2 - X-ray CT apparatus and image reconstruction method - Google Patents
X-ray CT apparatus and image reconstruction method Download PDFInfo
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- US9123156B2 US9123156B2 US13/824,697 US201113824697A US9123156B2 US 9123156 B2 US9123156 B2 US 9123156B2 US 201113824697 A US201113824697 A US 201113824697A US 9123156 B2 US9123156 B2 US 9123156B2
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- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
- G06T11/00—2D [Two Dimensional] image generation
- G06T11/003—Reconstruction from projections, e.g. tomography
- G06T11/006—Inverse problem, transformation from projection-space into object-space, e.g. transform methods, back-projection, algebraic methods
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- A—HUMAN NECESSITIES
- A61—MEDICAL OR VETERINARY SCIENCE; HYGIENE
- A61B—DIAGNOSIS; SURGERY; IDENTIFICATION
- A61B6/00—Apparatus for radiation diagnosis, e.g. combined with radiation therapy equipment
- A61B6/02—Devices for diagnosis sequentially in different planes; Stereoscopic radiation diagnosis
- A61B6/03—Computerised tomographs
- A61B6/032—Transmission computed tomography [CT]
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- A—HUMAN NECESSITIES
- A61—MEDICAL OR VETERINARY SCIENCE; HYGIENE
- A61B—DIAGNOSIS; SURGERY; IDENTIFICATION
- A61B6/00—Apparatus for radiation diagnosis, e.g. combined with radiation therapy equipment
- A61B6/52—Devices using data or image processing specially adapted for radiation diagnosis
- A61B6/5205—Devices using data or image processing specially adapted for radiation diagnosis involving processing of raw data to produce diagnostic data
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- A—HUMAN NECESSITIES
- A61—MEDICAL OR VETERINARY SCIENCE; HYGIENE
- A61B—DIAGNOSIS; SURGERY; IDENTIFICATION
- A61B6/00—Apparatus for radiation diagnosis, e.g. combined with radiation therapy equipment
- A61B6/52—Devices using data or image processing specially adapted for radiation diagnosis
- A61B6/5258—Devices using data or image processing specially adapted for radiation diagnosis involving detection or reduction of artifacts or noise
- A61B6/5264—Devices using data or image processing specially adapted for radiation diagnosis involving detection or reduction of artifacts or noise due to motion
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- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
- G06T2211/00—Image generation
- G06T2211/40—Computed tomography
- G06T2211/424—Iterative
Definitions
- the present invention relates to an X-ray CT apparatus that reconstructs an image using an iterative approximation method.
- the X-ray CT apparatus is an apparatus that obtains a tomographic image of an object by irradiating the object with fan-beam shaped X-rays or cone-beam shaped X-rays (conical or pyramid beam shaped X-rays), measuring X-rays transmitted through the object using an X-ray detector, and reconstructing the measurement data from multiple directions.
- Image reconstruction methods in the X-ray CT apparatus are largely divided into an analysis method and an iterative approximation method.
- the analysis method is a method of solving a problem analytically on the basis of a projection cutting plane theorem.
- the iterative approximation method is a method of mathematically modeling an observation system that has acquired the projection data and estimating the best image with a repetition method on the basis of the mathematical model.
- the advantage of the analysis method is that the amount of computation is overwhelmingly small since a reconstructed image is directly obtained from the actual projection data.
- the advantage of the iterative approximation method is that the quantum noise on the image or artifacts (such as cone beam artifacts) generated in the analysis method can be reduced since the physical process up to the acquisition of projection data and statistical fluctuations included in the actual projection data can be considered as a mathematical model and a statistical model, respectively.
- the Feldkamp method that is an analysis method or an improved method of the Feldkamp method has been mainly used due to the small amount of computation.
- practical applications of the iterative approximation method are also beginning to be considered with the development of high-performance computers in recent years.
- the iterative approximation method is a method of setting the evaluation index of an image in advance and updating the image iteratively so that the evaluation value obtained by quantifying the evaluation index takes a maximum or minimum value.
- the evaluation index discrepancy between actual projection data and forward projection data obtained by converting an image into projection data in the update process, stochastic plausibility, or the like is used.
- a function for calculating the evaluation value is called an evaluation function.
- NPL 1 An iterative approximation method using a penalized weighted least-square error function as an evaluation function has been proposed in NPL 1.
- matrices that are transposed matrices of each other in forward projection processing and back projection processing are generally applied as proposed in NPL 1.
- view-direction weighted back projection processing the back projection processing in which the view-direction weight is used.
- the view-direction weighted back projection processing itself has been proposed in NPL 3, and is a technique used in the analysis method.
- the view-direction weighted back projection processing has the following advantages.
- a relaxation coefficient related to the speed and stability of convergence in the iterative approximation method is included in the update expression for iterative update. It is necessary to set the relaxation coefficient in a specific range for stable convergence in the iterative approximation method.
- NPL 2 discloses that the relaxation coefficient is determined experientially.
- a method of calculating the relaxation coefficient using a power law has been proposed in NPL 4.
- the power law is an iterative solution technique to calculate the maximum eigenvalue of a certain matrix.
- PTL 1 discloses a method of generating virtual row data and virtual channel data by extending actual projection data and then performing back projection processing in the analysis method. If the method disclosed in PTL 1 can be applied to the iterative approximation method, it is possible to relax the restriction of the region.
- the degradation of image quality due to the movement of an object can be reduced by using the view-direction weighted back projection processing in the iterative approximation method, as in the method disclosed in NPL 2.
- NPL 2 there is a problem caused by an operator determining the relaxation coefficient experientially.
- a sufficient condition of the relaxation coefficient for the convergence in the iterative approximation method changes depending on the bed movement speed, scanning FOV (Field Of View), or the like as scanning conditions. It is very cumbersome and time consuming that the operator determines the relaxation coefficient experientially depending on a large number of these scanning conditions.
- the relaxation coefficient is set as a small value, the convergence condition of iterative approximation processing is satisfied regardless of scanning conditions due to the characteristic of the update matrix.
- convergence of iterative approximation processing becomes slow. As a result, the quality of a reconstructed image is also degraded.
- the present invention has been made in view of the above-described problem, and it is a first object of the present invention to provide an X-ray CT apparatus and the like that reconstruct an image using an iterative approximation method which ensures stable convergence and can be executed at high speed.
- a second object is to provide an X-ray CT apparatus and the like capable of suppressing the degradation of image quality when the iterative approximation method is applied to the data including the body movement.
- a third object is to provide an X-ray CT apparatus and the like capable of suppressing the degradation of image quality when the iterative approximation method is applied under the scanning conditions in which data loss occurs at the time of an axial scan or a spiral scan of high bed movement speed.
- a first invention is an X-ray CT apparatus that reconstructs a tomographic image of an object using an iterative approximation method to apply matrices that are not transposed matrices of each other in forward projection processing and back projection processing.
- the X-ray CT apparatus includes: a scanning unit that acquires actual projection data of the object on the basis of scanning conditions; and a computation unit that reconstructs the tomographic image by performing iterative approximation on the actual projection data using the scanning conditions and an update expression of the iterative approximation method including a relaxation coefficient that determines convergence of computation.
- the relaxation coefficient is analytically calculated on the basis of the scanning conditions.
- a second invention is an image reconstruction method of reconstructing a tomographic image of an object using an iterative approximation method to apply matrices that are not transposed matrices of each other in forward projection processing and back projection processing.
- the image reconstruction method includes: a step of acquiring actual projection data of the object on the basis of scanning conditions; and a step of reconstructing the tomographic image by performing iterative approximation on the actual projection data using the scanning conditions and an update expression of the iterative approximation method including a relaxation coefficient that determines convergence of computation.
- the relaxation coefficient is analytically calculated on the basis of the scanning conditions.
- an X-ray CT apparatus and the like that reconstruct an image using the iterative approximation method which ensures stable convergence and can be executed at high speed.
- an X-ray CT apparatus capable of suppressing the degradation of image quality when the iterative approximation method is applied to the data including the body movement.
- an X-ray CT apparatus and the like capable of suppressing the degradation of image quality when the iterative approximation method is applied under the scanning conditions in which data loss occurs at the time of an axial scan or a spiral scan of high bed movement speed.
- FIG. 1 is an external view of an entire X-ray CT apparatus 1 .
- FIG. 2 is a block diagram of the X-ray CT apparatus 1 .
- FIG. 3 is a diagram illustrating an axial scan and a spiral scan.
- FIG. 4 is a diagram illustrating a scanFOV 41 .
- FIG. 5 is a diagram illustrating a difference in the scanFOV 41 due to a difference in the bed movement speed.
- FIG. 6 is a diagram illustrating a correlation between an observed view and an opposite phase view.
- FIG. 7 is a diagram illustrating a view-direction weight.
- FIG. 8 is a flow chart showing the relaxation coefficient calculation process.
- FIG. 9 is a diagram illustrating an extension scanFOV.
- FIG. 10 is a flow chart showing data extension type back projection processing.
- FIG. 11 is a diagram illustrating the processing of calculating the number of extension rows.
- FIG. 12 is a diagram illustrating the FOM size.
- the X-ray CT apparatus 1 includes a scanner 2 (scanning unit) in which an X-ray tube 11 and a detector 12 are mounted, abed 4 on which an object 10 is placed, a computation device 5 (computation unit) that performs processing on the data obtained from the detector 12 , an input device 6 such as a mouse, a track ball, a keyboard, and a touch panel, and a display device 7 that displays a reconstructed image and the like.
- a scanner 2 scanning unit
- abed 4 on which an object 10 is placed a computation device 5 (computation unit) that performs processing on the data obtained from the detector 12
- an input device 6 such as a mouse, a track ball, a keyboard, and a touch panel
- a display device 7 that displays a reconstructed image and the like.
- An operator inputs scanning conditions, reconstruction parameters, or the like through the input device 6 .
- the scanning conditions include bed movement speed, tube current, tube voltage, and slice position.
- the reconstruction parameters include a region of interest, reconstructed image size, back projection phase width, and a reconstruction filter function.
- the X-ray CT apparatus 1 is configured to mainly include the scanner 2 , an operating unit 3 , and the bed 4 .
- the scanner 2 is configured to include the X-ray tube 11 (X-ray generator), the detector 12 , a collimator 13 , a driving device 14 , a central controller 15 , an X-ray controller 16 , a high voltage generator 17 , a scanner controller 18 , a bed controller 19 , a bed movement measuring device 20 , a collimator controller 21 , a preamplifier 22 , and an A/D converter 23 .
- the central controller 15 receives an input of scanning conditions or reconstruction parameters from the input device 6 in the operating unit 3 , and transmits control signals required for scanning to the collimator controller 21 , the X-ray controller 16 , the scanner controller 18 , and the bed controller 19 .
- the collimator controller 21 controls the position of the collimator 13 on the basis of the control signal.
- the X-ray controller 16 controls the high voltage generator 17 on the basis of the control signal.
- the high voltage generator 17 applies a tube voltage and a tube current to the X-ray tube 11 (X-ray generator).
- X-ray generator X-ray generator
- electrons of energy corresponding to the applied tube voltage are emitted from the cathode, and the emitted electrons collide with a target (anode).
- the object 10 is irradiated with X-rays of energy corresponding to the electron energy.
- the scanner controller 18 controls the driving device 14 on the basis of the control signal.
- the driving device 14 rotates a gantry unit, in which the X-ray tube 11 , the detector 12 , the preamplifier 22 , and the like are mounted, around the object 10 .
- the bed controller 19 controls the bed 4 on the basis of the control signal.
- X-rays emitted from the X-ray tube 11 are absorbed (attenuated) into each tissue in the object 10 according to the X-ray attenuation coefficient after the irradiation region is restricted by the collimator 13 , and the X-rays are transmitted through the object 10 and detected by the detector 12 disposed at the position facing the X-ray tube 11 .
- the detector 12 is formed by a plurality of detection elements disposed in a two-dimensional direction (a channel direction and a row direction perpendicular to the channel direction). X-rays received by each detection element are converted into projection data (hereinafter, referred to as “actual projection data”).
- X-rays detected by the detector 12 are converted into a current, amplified by the preamplifier 22 , converted into digital data by the A/D converter 23 , subject to LOG conversion and calibration, and input to the computation device 5 as actual projection data.
- the computation device 5 is configured to include a reconstruction computation unit 31 , an image processing unit 32 , and the like.
- an input/output device 9 is configured to include the input device 6 , the display device 7 , a storage device 8 (storage unit), and the like.
- the reconstruction computation unit 31 generates a reconstructed image by performing image reconstruction processing using the actual projection data.
- the reconstruction computation unit 31 forms a tomographic image in a non-destructive manner as a distribution map of the X-ray attenuation coefficient of the inside of the object 10 by generating filter correction projection data by overlapping a reconstruction filter on the actual projection data of each view and performing back projection processing by applying a weight in a view direction (hereinafter, referred to as a “view-direction weight”) for the filter correction projection data.
- the reconstruction computation unit 31 stores the generated reconstructed image in the storage device 8 .
- the reconstruction computation unit 31 displays the reconstructed image on the display device 7 as a CT image.
- the image processing unit 32 performs image processing on the reconstructed image stored in the storage device 8 , and displays the image-processed reconstructed image on the display device 7 as a CT image.
- Types of the X-ray CT apparatus 1 are largely divided into a multi-slice CT, which uses the detector 12 in which detection elements are arrayed in a two-dimensional direction, and a single-slice CT, which uses the detector 12 in which detection elements are arrayed in a row, that is, in a one-dimensional direction (only in a channel direction).
- a multi-slice CT X-ray beams spreading in a conical shape or in a pyramid shape are irradiated from the X-ray tube 11 , which is an X-ray source, according to the detector 12 .
- X-ray beams spreading in a fan shape are irradiated from the X-ray tube 11 .
- X-rays are irradiated while the gantry unit is rotating around the object 10 placed on the bed 4 (however, except for scanogram imaging).
- a scanning in which the bed 4 is fixed and the X-ray tube 11 rotates around the object 10 in the shape of circular orbit is called an axial scan or the like.
- a scanning in which the bed 4 moves and the X-ray tube 11 rotates around the object 10 in the shape of spiral orbit is called a spiral scan or the like.
- the bed controller 20 maintains the bed 4 in a stationary state.
- the bed controller 20 performs parallel movement of the bed 4 in a body axis direction according to the bed movement speed as the scanning conditions input through the input device 6 .
- the X-ray CT apparatus 1 is a multi-slice CT, for example.
- the scanning method of the X-ray CT apparatus 1 is a rotate-rotate method (third generation), for example.
- image reconstruction processing which is a prerequisite for each embodiment, will be described with reference to FIGS. 4 and 5 .
- an iterative approximation method using a penalized weighted least-square error function as an evaluation function and (2) an iterative approximation method of performing view-direction weighted back projection processing will be described.
- X (k) is a vector (image vector) indicating an image in the k-th iterative update
- y is a vector indicating actual projection data.
- A is a matrix that maps an image and projection data, and is called a system matrix since this expresses the characteristics of a scanning system through the above-described mathematical model.
- a T indicates a transposed matrix of A.
- Ax (k) is equivalent to processing (forward projection processing) to convert the image vector X (k) into a projection data vector.
- a T (.) is equivalent to processing (back projection processing) to convert the projection data vector in parentheses into an image vector.
- D is a diagonal matrix having a weight coefficient, which is weighted to the difference value between the actual projection data and the forward projection data, as a diagonal element.
- a value corresponding to the number of detected photons is assumed to be the weight coefficient.
- ⁇ is an arbitrary parameter that adjusts the strength of a penalty term.
- the penalty term serves to suppress the high frequency enhancement effect of the image by application of the iterative approximation method.
- S is a matrix having an inverse of each element of a vector s, which is expressed by the following expression, as a diagonal element.
- c is a vector that has the number of elements equal to that of the image vector and that has 1 as values of all elements.
- R in expression (1) and R′ in expression (2) are linear operators of the first derivative and the second derivative of the penalty term, and both are transformation matrices from an image vector to an image vector.
- l mn is an inverse of the distance between the m-th pixel and the n-th pixel.
- the quadratic function is used as a penalty term is shown as an example.
- a matrix Q in expression (7) is called an update matrix.
- the update matrix is a matrix to determine an update amount and an update direction of an image per one iterative update processing on the basis of update expression.
- I indicates a unit matrix.
- the spectral radius of the update matrix is ⁇ (Q)
- an image vector x (k+1) in expression (6) converges on expression (9) shown below under the conditions of expression (8) shown below.
- the spectral radius of the matrix is a least upper bound of the absolute value of the eigenvalue of the matrix.
- (.) ⁇ 1 indicates an inverse matrix of the matrix in parentheses.
- the spectral radius p (Q) shown in expression (8) is calculated and the relaxation coefficient ⁇ is set by calculating the maximum eigenvalue of the update matrix using the power law.
- the power law is not a method for solving the problem analytically, and computation time is increased since it is necessary to compute the large matrix operations sequentially.
- FIG. 4( a ) shows the arrangement of the X-ray tube 11 and the detector 12 on the scanning cross-section.
- FIG. 4( a ) shows a scanFOV 41 on the scanning cross-section.
- the scanFOV 41 is a region where an image is formed on the basis of the projection cutting plane theorem.
- the scanFOV 41 on the scanning cross-section is almost circular.
- FIG. 4( b ) shows the arrangement of the X-ray tube 11 and the detector 12 in the body axis direction.
- FIG. 4( b ) shows the scanFOV 41 in the body axis direction.
- the scanFOV 41 in the body axis direction is a polygon, such as a triangle, a rectangle, or a pentagon, even though it changes with the bed movement speed.
- FIG. 5 shows a difference in the scanFOV 41 in the body axis direction due to the difference in the bed movement speed.
- FIGS. 5( a ) and 5 ( b ) are compared with each other, it can be seen that the width of the scanFOV 41 in the body axis direction decreases as the bed movement speed increases.
- the width of the scanFOV 41 in the body axis direction is smaller than a predetermined value, this means that a view of 180° required to reconstruct a certain tomographic image cannot be acquired and therefore a region where an image can be generated is restricted.
- the value of the relaxation coefficient for stable convergence in an iterative approximation method is analytically calculated before performing image reconstruction processing. Then, image reconstruction processing based on the iterative approximation method to perform view-direction weighted back projection processing is executed.
- the characteristics of a scan of the X-ray CT apparatus 1 shown below are used.
- FIG. 6 shows a transmission path of an observed view and a transmission path of an opposite phase view in the channel direction.
- FIG. 6( b ) shows a transmission path of an observed view and a transmission path of an opposite phase view in the row direction.
- data satisfying such a relationship will be called actual projection data of opposite phases.
- a scanning time difference occurs in the view direction of actual projection data since the data is collected while rotating the X-ray tube 11 and the detector 12 . If the bed movement speed is constant during the scanning, the scanning time difference is proportional to the distance between the position of the X-ray tube 11 in the body axis direction and the position of the image in the body axis direction.
- FIG. 7 is a conceptual diagram of the view-direction weight.
- the computation device 5 of the X-ray CT apparatus 1 adds, as the view-direction weight, a weight so as to become 1 when added between actual projection data of opposite phases according to the distance between the position of a slice, which includes an observed pixel, in the body axis direction and the position of the X-ray tube 11 in the body axis direction.
- the computation device 5 of the X-ray CT apparatus 1 applies the weight of 0 excluding a predetermined number of views on both sides of a view of the position of the X-ray tube 11 in the body axis direction, which is closest to an observed pixel in the body axis direction, as a view-direction weight.
- a view to which a weight, which is not 0, is given will be called a back projection view
- the number of back projection views will be called a back projection view number.
- An appropriate value of the back projection view number is determined by the spiral pitch (value determined by the bed movement speed and the gantry rotation speed as scanning conditions) and the length of the detector 12 in the row direction.
- the view-direction weight By defining the view-direction weight in this manner, it is possible to improve the time resolution compared with a case where the view-direction weight is not used. This is because the time phases of multiple views contributing to image reconstruction processing are almost equal due to the view-direction weight.
- the definition of the view-direction weight it is possible to use a common back projection view number in all pixels and determine a central view for each slice, in the same manner as in the Feldkamp method.
- the definition of the view-direction weight it is also possible to determine a central view for each pixel as disclosed in “JP-A-2004-199163”.
- the definition of the view-direction weight it is also possible to determine the back projection view number in each pixel.
- the view-direction weight is defined as w ij since it is set for each element of the vector of the actual projection data and the image vector.
- b w ij a ij (10)
- a back projection matrix indicating the view-direction weighted back projection processing is B T .
- the system matrix A is a matrix that maps an image and projection data.
- the computation device 5 of the X-ray CT apparatus 1 calculates each element a ij on the basis of the apparatus specification of the X-ray CT apparatus 1 and the scanning conditions input through the input device 6 .
- a Joseph method proposed in “Joseph, P. M. (1982). An Improved Algorithm for Reprojecting Rays Through Pixel Images. IEEE Transactions on Medical Imaging MI-1, 192-196.” may be mentioned.
- Beam pitch (value obtained by dividing the bed movement speed by the row-direction detector size at the center of rotation): “value equivalent to high speed” or “value equivalent to low speed”, and the like
- the number of dimensions I of the vector of the actual projection data described above is determined from the apparatus specification and the scanning conditions. Specifically, I is “the number of elements in a row direction in the detector 12 ⁇ the number of elements in a channel direction in the detector 12 ⁇ the number of scanning views per rotation ⁇ the number of rotations in scanning”. Similarly, the number of dimensions J of the image vector is also determined from the scanning conditions. Specifically, J is “the number of pixels in a horizontal direction ⁇ the number of pixels in a vertical direction ⁇ the number of image slices”.
- the system matrix A is different between the case where the beam pitch which is one of the scanning conditions is the “value equivalent to high speed” and the case where the beam pitch which is one of the scanning conditions is the “value equivalent to low speed”. Therefore, the relaxation coefficient ⁇ for stable convergence in the iterative approximation method is also different.
- the operator norm of the update matrix is calculated instead of calculating the spectral radius of the update matrix.
- the operator norm of a matrix has the following characteristics.
- the present invention is not limited to this example, and can be applied to any iterative approximation method including an update matrix, in which the spectral radius can be adjusted using a relaxation coefficient, in the update expression.
- S is a matrix having an inverse of each element of a vector s, which is expressed by the following expression, as a diagonal element.
- the computation device 5 of the X-ray CT apparatus 1 add elements of a matrix I ⁇ (SB T DA+ ⁇ SR) in a row direction and set a maximum value in a row direction as the value of the operator norm ⁇ I ⁇ ( SB T DA ⁇ SR ) ⁇ .
- the computation device 5 of the X-ray CT apparatus 1 calculates the relaxation coefficient ⁇ analytically on the basis of the scanning conditions. In this manner, the X-ray CT apparatus 1 can determine the relaxation coefficient ⁇ quickly and easily compared with the iterative solution of the eigenvalue problem represented by the power law.
- the relaxation coefficient ⁇ is determined on the basis of scanning conditions, it is possible to ensure the stability of the algorithm compared with a case where the relaxation coefficient ⁇ is determined experientially.
- the computation device 5 of the X-ray CT apparatus 1 calculates matrices A, B, D, R, and R′ in expression (17) on the basis of the scanning conditions input through the input device 6 (step 1 ).
- the computation device 5 calculates each element of the matrix I ⁇ (SB T DA+ ⁇ SR) (step 2 ).
- the computation device 5 calculates the operator norm ⁇ I ⁇ (SB T DA+ ⁇ SR) ⁇ of the matrix I ⁇ (SB T DA+ ⁇ SR) (step 3 ).
- the computation device 5 determines the relaxation coefficient ⁇ such that expression (17) (predetermined conditional expression) is satisfied (step 4 ).
- the computation device 5 of the X-ray CT apparatus 1 calculates the relaxation coefficient ⁇ analytically on the basis of the scanning conditions.
- the computation device 5 of the X-ray CT apparatus 1 reconstructs a tomographic image by performing iterative approximation on the actual projection data using the update expression of the iterative approximation method including the scanning conditions and the relaxation coefficient ⁇ .
- the update expression of the iterative approximation method in the first embodiment is expression (14).
- the relaxation coefficient is calculated such that expression (17) defined on the basis of the operator norm of the update matrix Q shown in expression (16) is satisfied. Accordingly, iterative update processing based on the update expression of expression (14) is stably converged.
- Expression (17) is an expression showing that the operator norm of the update matrix Q is smaller than 1.
- the computation device 5 of the X-ray CT apparatus 1 calculate the value of the relaxation coefficient ⁇ applied to expression (14) as a maximum value satisfying the conditional expression of expression (17). That is, it is preferable that the computation device 5 set the largest possible value within a range, which satisfies the conditional expression of expression (17), as the relaxation coefficient ⁇ applied to expression (14).
- back projection processing using the view-direction weight is performed.
- the computation device 5 reconstructs a tomographic image of the object 10 by calculating a view-direction weight to apply the weight of 0 excluding a predetermined number of views on both sides of a view of the X-ray tube position closest to an observed pixel in the body axis direction, calculating the back projection matrix B T applied as back projection processing using the view-direction weight, and performing iterative approximation on the actual projection data using the update expression of expression (14) to which the back projection matrix B T is applied.
- the computation device 5 of the X-ray CT apparatus 1 calculates the relaxation coefficient ⁇ on the basis of the scanning conditions and performs iterative approximation on the actual projection data using the relaxation coefficient ⁇ calculated by itself.
- the device that performs the processing of calculating the relaxation coefficient ⁇ is not limited to the computation device 5 .
- the computation device 5 of the X-ray CT apparatus 1 or other computers perform the processing of calculating the relaxation coefficient ⁇ , which is shown in FIG. 8 , for each of various scanning conditions (for example, scanning conditions used to calculate the system matrix A described above) and store the calculation result in the storage device 8 of the X-ray CT apparatus 1 . That is, the storage device 8 stores the relaxation coefficient ⁇ for each of scanning conditions.
- the computation device 5 of the X-ray CT apparatus 1 searches for the setting value of the relaxation coefficient ⁇ stored in the storage device 8 using the scanning condition input through the input device 6 as a search key and performs iterative approximation on the actual projection data using the setting value of the relaxation coefficient ⁇ acquired as the search result.
- image reconstruction processing based on the iterative approximation method to perform data extension type back projection processing is executed using the relaxation coefficient ⁇ calculated analytically in the first embodiment.
- Such image reconstruction processing is effective when it is necessary to image a range, which is long in the body axis direction of the object 10 , in a predetermined time.
- image reconstruction processing is effective when shortening the scanning time takes priority over the quality of an image in a situation of a medical emergency.
- An object of the data extension type back projection processing is to extend projection data in the channel and row directions and expand the scanFOV 41 using the virtual projection data (hereinafter, referred to as “extended projection data”), as shown in FIG. 9 .
- extended projection data the virtual projection data
- the scanFOV 41 extended by applying the data extension type back projection processing will be called “extension scanFOV” hereinbelow.
- FIG. 9( a ) shows an extension in the channel direction.
- Extension channels 42 a and 42 b are projection data extended in the channel direction.
- a channel-direction extension scanFOV 43 is obtained by extending the scanFOV 41 by application of the data extension type back projection processing using the extension channels 42 a and 42 b.
- FIG. 9( b ) shows an extension in the row direction.
- An extension row 44 is projection data extended in the row direction.
- a row-direction extension scanFOV 45 is obtained by extending the scanFOV 41 by application of the data extension type back projection processing using the extension row 44 .
- the computation device 5 of the X-ray CT apparatus 1 performs the processing of calculating the number of extension rows and the number of extension channels on the basis of the scanning conditions input through the input device 6 (step 11 ).
- a distance between the X-ray tube 11 and the center of rotation is set to d sod .
- a distance between the X-ray tube 11 and the center (detector center 52 ) of the detector 12 is set to d sid .
- an FOM size which is the size of FOM (Field Of Measurement) 51 is set to d ⁇ .
- the FOM size d ⁇ is twice the distance between the center of rotation and an apex 54 , which is farthest from the center of rotation, among the apices of a reconstruction FOV 53 (image region to be generated), as shown in FIG. 12 .
- the opening width of a detection element in the body axis direction is d dtc
- the number of rows of a detection element is r re
- the number of extended rows is r im .
- a straight line connecting the X-ray tube 11 and the detector center 52 is set to the q axis. Since the length of a row of detection elements is constant, the number of extension rows is determined by calculating r im .
- X-ray tube side plane a plane close to the X-ray tube 11 (hereinafter, referred to as “X-ray tube side plane”) between two planes, which are perpendicular to the q axis and are in contact with an FOM 51 , is focused.
- d s the crossing length of the X-ray tube side plane and an X-ray beam in the body axis direction is d s .
- F is a back projection phase width.
- F is a parameter for adjusting trade-offs between the degradation of image quality due to estimation error of extended projection data and the degradation of image quality due to the loss of actual projection data.
- r im d sid ⁇ ⁇ ⁇ [ F + ⁇ ⁇ / ( 2 ⁇ ⁇ ) ⁇ ] d dtc ⁇ ⁇ d sod - ( d ⁇ / 2 ) ⁇ - r re ( 20 )
- the computation device 5 of the X-ray CT apparatus 1 calculates the number of extended rows r im according to expression (20).
- the computation device 5 extend a channel so as to contain the extension scanFOV 43 within the scanning cross-section. In this case, the number of extension channels can be easily calculated.
- the computation device 5 performs processing of generating the extended projection data on the basis of the number of extension rows and the number of extension channels calculated in step 11 (step 12 ).
- step 12 The processing of generating the extended projection data in step 12 will be described.
- extended projection data in the row direction is estimated by extrapolation from the difference data between forward projection data and actual projection data.
- extended projection data in the row direction is estimated by zero-order extrapolation using data, which is located on the outermost side in the row direction, of data obtained as actual projection data.
- the computation device 5 of the X-ray CT apparatus calculates the projection value ⁇ of the extended projection data according to expression (21).
- the computation device 5 performs back projection processing by combining the actual projection data of the object 10 acquired by the scanner 2 and the extended projection data generated in step 12 (step 13 ).
- B T ( A T +ZP ) (22)
- the iterative approximation method of performing data extension type back projection processing can be formulized by substituting expression (22) into expression (14).
- the present invention may also be applied to an axial scan.
- the projection data has been extended in the channel and row directions, the projection data may also be extended in only one of the channel and row directions.
- the back projection processing is performed using the extended projection data obtained by extending the actual projection data in the channel direction and/or the row direction.
- the computation device 5 of the X-ray CT apparatus 1 calculates the relaxation coefficient ⁇ analytically on the basis of the scanning conditions input through the input device 6 , as in the first embodiment.
- back projection processing is performed using the extended projection data, which is obtained by extending the actual projection data in the channel direction and/or the row direction, and the view-direction weight.
- the computation device 5 of the X-ray CT apparatus 1 calculates the relaxation coefficient ⁇ analytically on the basis of the scanning conditions input through the input device 6 , as in the first embodiment.
- the computation device 5 calculates the transformation matrix P from the actual projection data to the extended projection data on the basis of the scanning conditions input through the input device 6 .
- the computation device 5 calculates a view-direction weight to apply the weight of 0 excluding a predetermined number of views on both sides of a view of the X-ray tube position closest to an observed pixel in the body axis direction, and calculates the back projection matrix B T applied as back projection processing using the view-direction weight.
- the computation device 5 reconstructs a tomographic image by calculating an extended back projection matrix, which is applied as back projection processing in which the actual projection data and the extended projection data are combined, using the transformation matrix P and the view-direction weight and performing iterative approximation on the actual projection data and the extended projection data using the update expression of expression (14) to which the extended back projection matrix is applied.
Abstract
Description
-
- (1) Redundancy of projection data can be eliminated.
- (2) Time resolution can be improved.
- [PTL 1] JP-A-2009-90139
- [NPL 1] H. Erdogan et. al., “Ordered subsets algorithms for transmission tomography,” Phys. Med. Biol., Vol. 44, pp. 2835-2851, 1999
- [NPL 2] J. Sunnegardh, “Combining analytical and iterative reconstruction in helicalcone-beam CT,” “Linkoping Studies in Science and Technology Thesis No. 1301, 2007
- [NPL 3] S. Wesarg et. al., “Parker weights revisited,” Med. Phys. Vol. 29, No. 3, pp 372-378, March 2002
- [NPL 4] G. L. Zeng and G. T. Gullberg, “Unmatched projector/backprojector pairs in an iterative reconstruction algorithm” IEEE. Trans. Med. Imag, Vol. 19, No. 5, pp 548-555, May 2000
x (k+1) =x (k) +S[A T D(y−Ax (k))+βRx (k)] (1)
s=(A T DA+βR′)c (2)
x (k+1) =x (k) +αB T(y−Ax (k))+αβRx (k) (5)
-
- α is a relaxation coefficient related to the speed and stability of convergence in the iterative approximation method. When matrices that are not transposed matrices of each other in forward projection processing and back projection processing are applied (in the case of A≠B), it is necessary to set the relaxation coefficient in the range of a specific value for stable convergence in the iterative approximation method.
x (k+1) =Qx (k) +αB T y (6)
Q=I−αB T A+αβR (7)
b ij =w ij a ij (10)
-
- The number of elements in a row direction in the
detector 12 - The number of elements in a channel direction in the
detector 12 - The size of one element in a row direction in the
detector 12 - The size of one element in a channel direction in the
detector 12 - Distance dsod between the
X-ray tube 11 and the center of rotation - Distance dsid between the
X-ray tube 11 and the center (detector center) of thedetector 12
- The number of elements in a row direction in the
-
- The number of rotations in scanning
- Angle at the start of scanning
- Rotation speed
- The number of scanning views per rotation
- Scanning method: “axial scan” or “spiral scan”, or the like
- The number of pixels (within a cross-section): the number of pixels in a horizontal direction×the number of pixels in a vertical direction
- The number of image slices
- Pixel size (within a cross-section)
- Image slice thickness
- Image center position (within a cross-section): “matched with the center of rotation” or the like
- Center position in an image slice direction: “matched with the number of rotations in scanning of 2.5” or the like
ρ(C)≦∥C∥ (12)
∥Q∥<1 (13)
x (k+1) =x (k) +αS[B T D(y−Ax (k))+βRx (k)] (14)
s=(B T DA+βR′)c (15)
Q=I−α(SB T DA+βSB) (16)
∥I−α(SB T DA+βSR)∥<1 (17)
∥I−α(SB T DAαβSR)∥.
d t =κ[F+{φ/(2π)}] (19)
ψ=P(y−Ax) (21)
B T=(A T +ZP) (22)
-
- 1: X-ray CT apparatus
- 2: scanner
- 3: operating unit
- 4: bed
- 5: computation device
- 6: input device
- 7: display device
- 8: storage device
- 10: object
- 11: X-ray tube
- 12: detector
- 41: scanFOV
- 42 a, 42 b: extension channel
- 43: channel-direction extension scanFOV
- 44: extension row
- 45: row-direction extension scanFOV
- 51: FOM
- 52: detector center
- 53: reconstruction FOV
Claims (12)
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